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Proof step 23 from proof band-011x-eq (previous step)

0 ≤ j, 0 < j, 2 ^ i0 ≤ j, 0 ≤ i0 ⊦ (2 ^ i0 - j) % 2 ^ i0 + j % 2 ^ i0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i ∧ 0 ≤ j ∧ i ≤ j → (i - j) % i = ~(j % i) subst: [j, i] → [j, 2 ^ i0] rotate: F spec: int-div inst: name: mod-sub-01

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ~ i + i = 0;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < j → ¬ j < i; Used terms: j, 2 ^ i0